A300321 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 16, 16, 8, 13, 50, 61, 61, 50, 13, 21, 112, 186, 735, 186, 112, 21, 34, 348, 977, 3486, 3486, 977, 348, 34, 55, 1028, 3875, 25797, 31345, 25797, 3875, 1028, 55, 89, 2796, 15976, 203113, 345605, 345605, 203113, 15976, 2796, 89

Offset

1,2

Comments

Table starts

..1....2.....3........5.........8..........13............21...............34

..2....4.....4.......16........50.........112...........348.............1028

..3....4....16.......61.......186.........977..........3875............15976

..5...16....61......735......3486.......25797........203113..........1378779

..8...50...186.....3486.....31345......345605.......4705725.........55447293

.13..112...977....25797....345605.....8002885.....178277369.......3616312721

.21..348..3875...203113...4705725...178277369....7221094975.....257924884697

.34.1028.15976..1378779..55447293..3616312721..257924884697...16292595627604

.55.2796.69695.10140973.678378012.80381600442.9967764866344.1108503299923830

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 40] for n>43

Example

Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..1
..1..0..0..0. .1..0..0..0. .1..1..0..0. .1..1..1..1. .0..0..0..0
..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
..1..1..1..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..1
..1..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0. .1..0..1..1

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A299052 A299814 A299689 * A026254 A091525 A091524

Adjacent sequences: A300318 A300319 A300320 * A300322 A300323 A300324

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 02 2018

Status

approved